If we look at places like certain countries in Africa, Middle East, and Asia, it's there. Often at the hands of Muslims.
Sure. Like I said: it's rare. It does happen sometimes, but not often.
But Christians have certainly played their role and have not acted to end the cycles of butchery and vengeance.
Christianity also has a bunch of weird things going on, depending on the denomination.
We often get Christians who latch onto the idea of persecution as a mark of faith or God's approval, so it can cause a real crisis of faith to not be a suffering martyr for Christ. As a consequence, they feel the need to point to
anything - even if it doesn't actually involve any hardship at all - so they can say "the Bible said the faithful would be persecuted for their faith, and I'm 'persecuted,' so my faith is genuine."
There's also a strong thread through some branches of Christianity that they're meant to be in charge, or at least be able to impose themselves on non-Christian or have their religion acknowledged as special.
For these people, not being able to install a theocracy or finding out that their proselytizing is unwelcomed counts as "persecution."